UNIVERSITY OF HOUSTON

                      INSTITUTE FOR THEORETICAL
                                AND
                        ENGINEERING SCIENCE

                     NONLINEAR DYNAMICS SEMINAR


                            IAN MELBOURNE

                        Department of Mathematics
                        University of Surrey

                        Thursday, October 24, 2002
                             4:00-5:00 PM
                             Room 634 SR1

       A New Test for Chaos in Deterministic Nonlinear Dynamical Systems


Abstract

Recently, Georg Gottwald (Sydney) and I developed a new test for determining
whether a given deterministic dynamical system is chaotic or non chaotic;
this is an alternative to the usual approach of computing the largest
Lyapunov exponent.  Our method is a 0-1 test for chaos.  The output is a 0
signifying non-chaotic or a 1 signifying chaotic, and is independent of the
dimension of the dynamical system.  Moreover, the test is applied directly
to the time series data; so the underlying equations need not be known.  The
test works equally well for continuous and discrete time.
In this lecture, I will describe how the test is implemented and comparison
with the Lyapunov exponent method; describe why the test works based on
rigorous ergodic-theoretical results of Ashwin, Field, Nicol and myself.



This seminar is easily accessible to persons with disabilities.  For more
information or assistance, please contact the ITES office at (713) 743-3512
or the Mathematics Department at (713) 743-3500.

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        Future Nonlinear Dynamics and Neuroscience Seminars

November 14:    Charles Wilson (University of Texas at San Antonio)

November 15:    Rafael de la Llave (University of Texas at Austin)

November 21:    Fabrizio Gabbiani (Baylor College of Medicine)

December 5:     Richard Cai (Harvard University)